Growth Rate Calculations

• Growth of GDP is exponential since the Industrial Revolution
• Growth Rate is always quoted as the exponential growth rate $e^g$
• Growth rate itself is mostly constant

$$\begin{gathered} Y_t=Y_{t-1}\cdot e^g \\ {e}^g\approx \frac{Y_t}{Y_{t-1}}\approx \frac{Y_{t-n}}{Y_{t-n-1}} \end{gathered}$$

• Predicting growth into the future: $Y_{t-n}\cdot e^{n\cdot g}=Y_t$
• Adding growth rates: $g_x=g_y+g_z$ e.g. $Y^{\text{nominal}}=\text{Price Level}\cdot Y^{real}$ ⇒ $g^{Y\text{nominal}}=g^{\text{price level}}+g^{Y\text{real}}$
• Dividing growth rates: $g_a=g_b-g_c$ e.g. $\text{GDP per Capita}=\frac{Y}{\text{population}}$ ⇒ $g^{\text{GDP per Cap.}}=g^Y-g^{\text{population}}$
• function of growth rate: let $A=f(B)$ then $g_a=\frac{\partial A}{\partial B}\cdot \frac{B}{f(B)}\cdot g_b$ e.g.2. $Y=K^{\alpha }{N}^{1-\alpha }$ ⇒ elasticity $g^Y=\alpha g_{\alpha }+(1-\alpha )g_N$